Stability of peakons for the Degasperis-Procesi equation

Details Stability of peakons for the Degasperis-Procesi equation Stability of peakons for the Degasperis-Procesi equation

2007-12-12

arxiv.org/abs/0712.2007v1

Mathematics

Analysis of PDEs

21 pages, to appear in Comm. Pure Appl. Math

Scientific paper

The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa-Holm equation. In this paper, we study the orbital stability problem of the peaked solitons to the Degasperis-Procesi equation on the line. By constructing a Liapunov function, we prove that the shapes of these peakon solitons are stable under small perturbations.

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